Chapter 33

If $f(x)=4x^2-3x+2$ find: $f(0),f(3),f(-1)$ and $f(3)-f(-1)$

Given that $f(x)=5x^2+x-7$ determine: (i) $f(2)÷f(1)$ (ii) $f(3+a)$ (iii) $f(3+a)-f(3)$ (iv) $\frac{f(3+a)-f(3)}{a}$

Differentiate from first principles $f(x)=x^2$ and determine the value of the gradient of the curve at $x=2$

Find the differential coefficient of $y=5x$

Find the derivative of $y=8$

Differentiate from first principles $f(x)=2x^3$

Find the differential coefficient of $y=$ $4x^2+5x-3$ and determine the gradient of the curve at $x=-3$

Using the general rule, differentiate the following with respect to $x$ : (a) $y=5x^7$ (b) $y=3\sqrt{x}$ (c) $y=\frac{4}{x^2}$

Find the differential coefficient of $y=\frac{2}{5}{x}^3-\frac{4}{x^3}+4\sqrt{x^5}+7$

If $f(t)=5t+\frac{1}{\sqrt{t^3}}$ find $f^{\prime }(t)$